Four hundred eighty dollars are available to fence in a rectangular garden. the fencing for the north and south sides of the garden costs $10 per foot and the fencing for the east and west sides costs $15 per foot. find the dimensions of the largest possible garden. (give exact answers.)

The rectangle will be its largest when the cost of the north/south fencing is equal to the cost of the east/west fencing, and both are half the total.

The north and south dimensions will be ($480/2)/($10/ft)/2 = 12 ft.

The east and west dimensions will be ($480/2)/($15/ft)/2 = 8 ft.

The largest possible garden is 12 ft in the north-south direction by 8 ft in the east-west direction.

Let p represent the cost per foot in the x direction, and let q represent the cost per foot in the y direction. Then the total cost is

... C = 2px + 2qy

and the area is

... A = xy

In terms of x, the area is

... A = x(C -2px)/(2q)

This describes a downward-opening parabola whose vertex is at x=C/(4p). That is, the value of x will be C/(4p) and the cost in the x-direction will be

.. 2px = 2p(C/(4p)) = C/2

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950